Unit Rate Formula, Definition, Solved Examples

The Unit Rate Formula explains how to calculate a unit rate, which is a ratio comparing different quantities with distinct units, like miles per hour or dollars per ounce. The term "per" in these ratios suggests a rate comparison. This "per" can be symbolized by "/" in calculations. Essentially, a unit rate involves comparing a quantity to its specific unit of measurement, and this can be determined using the unit rate formula.

What is the Unit Rate Formula?

The unit rate formula defines a rate where the denominator is 1, comparing a quantity to its corresponding unit of measurement. For instance, if someone runs three miles in 30 minutes, their rate is one mile per 10 minutes. Expressing miles per minute illustrates the distance covered in a specific time unit. Unit rates are always represented as a quantity of 1.

Exploring real-life applications of unit rates:

Time-based rates: Distance covered per time unit, average speed (miles/hour), and interest rates (simple or compound)

Cost comparisons: Cost per pound, quantity for a specific cost (e.g., 20 oz of juice for 4 dollars), or for comparing prices.

Additional examples include literacy rates, population metrics, and other data-driven rates.

The unit rate formula to determine the rate between two quantities a and b is as follows:

Unit Rate = Ratio between two distinct quantities with different units

= a:b

= a/b

Definition of Unit Rate

A unit rate is characterized as the ratio between two measurements, where the second term equals 1. It distinguishes itself from a standard rate, where a specific number of units from the first quantity is compared to a single unit of the second quantity. For instance, considering that there are 60 seconds in one minute, a unit rate could be illustrated as 60 seconds per minute. In this case, "per minute" signifies one minute as the standard unit of comparison.

Formula for Unit Rate

The formula to determine the unit rate between two quantities, denoted as 'a' and 'b', can be expressed as follows:

Unit Rate = Ratio of two distinct quantities with differing units

= a:b

= a/b

Unit Rate Formula Solved Examples

Example 1: A delivery service transports 240 packages in 6 hours. Determine the rate of packages delivered per hour using the unit rate formula.

Solution:

Given:

Packages transported = 240 packages

Time taken = 6 hours

Let 'a' represent the quantity transported and 'b' the time taken.

To find: Quantity per hour

Using the unit rate formula: unit rate = a / b,

Packages delivered per hour = 240 / 6

= 40 packages/hour

Therefore, the rate of packages delivered per hour is 40 packages.

Example 2: A car travels 360 miles using 12 gallons of fuel. Find the car's miles per gallon using the unit rate formula.

Solution:

Given:

Distance traveled = 360 miles

Fuel used = 12 gallons

Let 'a' represent the distance and 'b' the amount of fuel.

To find: Miles per gallon

Using the unit rate formula: unit rate = a / b,

Miles per gallon = 360 miles / 12 gallons

= 30 miles/gallon

Hence, the car travels 30 miles per gallon of fuel.

Example 3: A factory produces 500 toys in 5 hours. Determine the rate of toy production per hour using the unit rate formula.

Solution:

Given:

Toys produced = 500 toys

Time taken = 5 hours

Let 'a' represent the quantity produced and 'b' the time taken.

To find: Quantity per hour

Using the unit rate formula: unit rate = a / b,

Toys produced per hour = 500 / 5

= 100 toys/hour

Therefore, the factory produces toys at a rate of 100 toys per hour.

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